Paolo Baldan

Contextual Petri nets, asymmetric event structures, and processes

We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (read-only operations). A basic role is played by asymmetric event structures, a generalization of Winskels prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskels seminal work on safe nets, the truly concurrent event-based semantics of contextual nets is given at categorical level via a chain of coreflections leading from the category SW-CN of semi-weighted contextual nets to the category Dom of finitary prime algebraic domains. First an unfolding construction generates from a contextual net a corresponding occurrence contextual net, from where an asymmetric event structure is extracted. Then the configurations of the asymmetric event structure, endowed with a suitable order, are shown to form a finitary prime algebraic domain. We also investigate the relation between the proposed unfolding semantics and several deterministic process semantics for contextual nets in the literature. In particular, the domain obtained via the unfolding is characterized as the collection of the deterministic processes of the net endowed with a kind of prefix ordering. 2001 Elsevier Science.

A Static Analysis Technique for Graph Transformation Systems

In this paper we introduce a static analysis technique for graph transformation systems. We present an algorithm which, given a graph transformation system and a start graph, produces a finite structure consisting of a hypergraph decorated with transitions (Petri graph) which can be seen as an approximation of the Winskel style unfolding of the graph transformation system. The fact that any reachable graph has an homomorphic image in the Petri graph and the additional causal information provided by transitions allow us to prove several interesting properties of the original system. As an application of the proposed technique we show how it can be used to verify the absence of deadlocks in an infinite-state Dining Philosophers system.

Petri nets for modelling metabolic pathways: a survey

In the last 15 years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net.

Approximating the Behaviour of Graph Transformation Systems

We propose a technique for the analysis of graph transformation systems based on the construction of finite structures approximating the behaviour of such systems with arbitrary accuracy. Following a classical approach, one can construct a chain of finite under-approximations (k-truncations) of the Winskels style unfolding of a graph grammar. More interestingly, also a chain of finite over-approximations (k-coverings) of the unfolding can be constructed and both chains converge (in a categorical sense) to the full unfolding. The finite over- and under-approximations can be used to check properties of a graph transformation system, like safety and liveness properties, expressed in (meaningful fragments of) the modal µ-calculus. This is done by embedding our approach in the general framework of abstract interpretation.

Compositional semantics for open Petri nets based on deterministic processes

In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalisation of the ordinary model where some places, designated as open, represent an interface between the system and the environment. Besides generalising the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the Goltz–Reisig process semantics of Petri nets. We introduce a composition operation over open nets, characterised as a pushout in the corresponding category, suitable for modelling both interaction through open places and synchronisation of transitions. The deterministic process semantics is shown to be compositional with respect to such a composition operation. If a net

Verifying Finite-State Graph Grammars: an Unfolding-Based Approach

Z_3

Unfolding and Event Structure Semantics for Graph Grammars

results as the composition of two nets

A framework for the verification of infinite-state graph transformation systems

Z_1

Domain and event structure semantics for Petri nets with read and inhibitor arcs

and

A logic for analyzing abstractions of graph transformation systems

Z_2